Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C7 |
| direct product | C32×C7⋊D133 |
| Fitting, socle, Hall | C32×C72×C19 ⋊ C2 |
| derived, Hall | C72×C19 ⋊ C2×C32 |
| Hall | C32×C72 ⋊ D19 |
| Hall | C32×C19 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ C32×D19 |
| Sylow | C19 ⋊ C32×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C7⋊D133 |
| commutator, cosocle, hypocenter | C72×C19 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C19 | C2 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C32 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8379 |
4203 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D7×D133, C32×D19×C7⋊D7, C3×D21⋊D133, … |
| maximal normal subgroup of | C32×D7×D133, C32×D19×C7⋊D7, C3×D21⋊D133, … |
| maximal quotient of | C32×C7⋊Dic133, C2×C32×C7⋊D133 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 414);